Polymorphic Sesqui-Pushout Graph Rewriting

Abstract

The paper extends Sesqui-Pushout Graph Rewriting (SqPO) by polymorphism, a key concept in object-oriented design. For this purpose, the necessary theory for rule composition and decomposition is elaborated on an abstract categorical level. The results are applied to model rule extension and type dependent rule application. This extension mechanism qualifies SqPO – with its very useful copy mechanism for unknown contexts – as a modelling technique for extendable frameworks. Therefore, it contributes to the applicability of SqPO in software engineering. A version management example demonstrates the practical applicability of the combination of context-copying and polymorphism.